具有相等Grundy支配和独立数的图

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Discrete Optimization Pub Date : 2023-05-01 DOI:10.1016/j.disopt.2023.100777
Gábor Bacsó , Boštjan Brešar , Kirsti Kuenzel , Douglas F. Rall
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Rall","doi":"10.1016/j.disopt.2023.100777","DOIUrl":null,"url":null,"abstract":"<div><p>The Grundy domination number, <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mi>gr</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>, of a graph <span><math><mi>G</mi></math></span> is the maximum length of a sequence <span><math><mrow><mo>(</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow></math></span> of vertices in <span><math><mi>G</mi></math></span> such that for every <span><math><mrow><mi>i</mi><mo>∈</mo><mrow><mo>{</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>}</mo></mrow></mrow></math></span>, the closed neighborhood <span><math><mrow><mi>N</mi><mrow><mo>[</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>]</mo></mrow></mrow></math></span> contains a vertex that does not belong to any closed neighborhood <span><math><mrow><mi>N</mi><mrow><mo>[</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>]</mo></mrow></mrow></math></span>, where <span><math><mrow><mi>j</mi><mo>&lt;</mo><mi>i</mi></mrow></math></span>. 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引用次数: 1

摘要

图G的Grundy支配数γgr(G)是G中顶点序列(v1,v2,…,vk)的最大长度,使得对于每i∈{2,…,k},闭邻域N[vi]包含不属于任何闭邻域N[fj]的顶点,其中j<;i.众所周知,任何图G的Grundy控制数都大于或等于上控制数Γ(G),而上控制数又大于或等于独立数α(G)。本文研究了Γ(G)=γgr(G)的图G的一类及其由α(G)=γgr(G)的图组成的子类。我们刻画了所有双自由连通图中的后一类图,给出了这些图的一些性质,并证明了超立方体是这类图的成员。此外,我们给出了Γ(G)=γgr(G)的图G的几个必要条件,并给出了这类图的大族。
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Graphs with equal Grundy domination and independence number

The Grundy domination number, γgr(G), of a graph G is the maximum length of a sequence (v1,v2,,vk) of vertices in G such that for every i{2,,k}, the closed neighborhood N[vi] contains a vertex that does not belong to any closed neighborhood N[vj], where j<i. It is well known that the Grundy domination number of any graph G is greater than or equal to the upper domination number Γ(G), which is in turn greater than or equal to the independence number α(G). In this paper, we initiate the study of the class of graphs G with Γ(G)=γgr(G) and its subclass consisting of graphs G with α(G)=γgr(G). We characterize the latter class of graphs among all twin-free connected graphs, provide a number of properties of these graphs, and prove that the hypercubes are members of this class. In addition, we give several necessary conditions for graphs G with Γ(G)=γgr(G) and present large families of such graphs.

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来源期刊
Discrete Optimization
Discrete Optimization 管理科学-应用数学
CiteScore
2.10
自引率
9.10%
发文量
30
审稿时长
>12 weeks
期刊介绍: Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.
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